1 Simulation set up

  • Sample size for both training and testing set is 200
  • 50 covariates, 10 groups, 5 covariates each group
  • group 1 and 3 are important, with beta = c(1, 2, 3, 4, 5)
  • signal-to-noise ratio = 1
  • use BIC to select lambda
  • use prediction error to evaluate prediction
  • tuning parameter of weight: 0, .25, .5, .75, 1, no scale. just used cost for weight
  • cost randomly generated with each simulation
  • solution path

2 zero correlation for both inter and intra group

2.1 Results

## # A tibble: 5 x 3
##   variable ave_pe med_pe
##   <fct>     <dbl>  <dbl>
## 1 Lasso      1.22   1.21
## 2 CRL        1.23   1.21
## 3 GL         1.14   1.13
## 4 CGL        1.15   1.14
## 5 rCGL       1.13   1.13
## # A tibble: 5 x 3
##   variable ave_cpp med_cpp
##   <fct>      <dbl>   <dbl>
## 1 Lasso       82.7    80.2
## 2 CRL         81.8    78.9
## 3 GL          64.5    62.3
## 4 CGL         61.8    60.3
## 5 rCGL        61.4    60.4

2.2 Solution path

3 zero between-group, 0.5 within group correlaion

3.1 Results

## # A tibble: 5 x 3
##   variable ave_pe med_pe
##   <fct>     <dbl>  <dbl>
## 1 Lasso      1.13   1.12
## 2 CRL        1.14   1.13
## 3 GL         1.13   1.12
## 4 CGL        1.14   1.14
## 5 rCGL       1.13   1.12
## # A tibble: 5 x 3
##   variable ave_cpp med_cpp
##   <fct>      <dbl>   <dbl>
## 1 Lasso       49.9    45.3
## 2 CRL         51.4    46.3
## 3 GL          64.6    62.9
## 4 CGL         61.9    60.6
## 5 rCGL        62.2    61.1

3.2 Solution path

4 0.5 correlation for both between and within groups

4.1 Results

## # A tibble: 5 x 3
##   variable ave_pe med_pe
##   <fct>     <dbl>  <dbl>
## 1 Lasso      1.13   1.13
## 2 CRL        1.14   1.13
## 3 GL         1.14   1.14
## 4 CGL        1.16   1.16
## 5 rCGL       1.14   1.13
## # A tibble: 5 x 3
##   variable ave_cpp med_cpp
##   <fct>      <dbl>   <dbl>
## 1 Lasso      117.    118. 
## 2 CRL        105.    108. 
## 3 GL          85.8    86.7
## 4 CGL         86.2    86.2
## 5 rCGL        80.7    79.8

4.2 Solution path